Optimization Problem Setup

Choose solver, define objective function and constraints, compute in parallel

For linear programming and mixed-integer linear programming, choose between this solver-based approach and a problem-based approach. See Linear Programming and Mixed-Integer Linear Programming.

To represent your optimization problem for solution in this solver-based approach, you generally follow these steps:

• Choose an optimization solver.

• Create an objective function, typically the function you want to minimize.

• Create constraints, if any.

• Set options, or use the default options.

• Call the appropriate solver.

For a basic nonlinear optimization example, see Solve a Constrained Nonlinear Problem. For a basic mixed-integer linear programming example, see Mixed-Integer Linear Programming Basics: Solver-Based.

Featured Examples

Tutorial for the Optimization Toolbox™

Tutorial for the Optimization Toolbox™

This example shows how to use two nonlinear optimization solvers and how to set options. The nonlinear solvers that we use in this example are fminunc and fmincon.
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Nonlinear Data-Fitting

Nonlinear Data-Fitting

This example shows how to fit a nonlinear function to data using several Optimization Toolbox™ algorithms.
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Traveling Salesman Problem: Problem-Based

Traveling Salesman Problem: Problem-Based

This example shows how to use binary integer programming to solve the classic traveling salesman problem. This problem involves finding the shortest closed tour (path) through a set of stops (cities). In this case there are 200 stops, but you can easily change the nStops variable to get a different problem size. You'll solve the initial problem and see that the solution has subtours. This means the optimal solution found doesn't give one continuous path through all the points, but instead has several disconnected loops. You'll then use an iterative process of determining the subtours, adding constraints, and rerunning the optimization until the subtours are eliminated.
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